SimplePendulum

SimplePendulum - Simple Pendulum Spreadsheet Michael...

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Simple Pendulum Spreadsheet Michael Fowler, University of Virginia We consider the case of a simple pendulum in which the string is replaced by a light rod, which is constrained to move in a vertical circle. In other words, this pendulum can "loop the loop", going over the top, where a string one would slacken. The rod has length L, and is at angle theta relative to vertical y down, so the force on the pendulum in the direction of motion is -mg sin theta. This equals md2s/dt2 = mLd2 theta/dt2. Ld2 theta/dt2 = -gsin theta We cal the angular velocity omega, and the angular acceleration alpha. Click on and change the red numbers below! (See Sheet 2 for a brief discussion of the construction of the table below from the dif erential equation.) L= 1 length of pendulum g= 9.8 gravity theta_init= 0.1 initial position omega_init= 0 initial velocity delta_t= 0.02 time interval in seconds midway time theta omega alpha 0 0.1 0 -0.978367 0.02 0.099804 -0.009784 -0.976459 0.04 0.099218 -0.029313 -0.970743 0.06 0.098244 -0.048728 -0.961238 0.08 0.096884 -0.067952 -0.947983 0.1 0.095146 -0.086912 -0.931027 0.12 0.093036 -0.105533 -0.910434 0.14 0.090561 -0.123741 -0.886283 0.16 0.087731 -0.141467 -0.858665 0.18 0.084559 -0.15864 -0.827687 0.2 0.081055 -0.175194 -0.793467 0.22 0.077233 -0.191063 -0.756136 0.24 0.07311 -0.206186 -0.715837 0.26 0.0687 -0.220503 -0.672727 0.28 0.064021 -0.233957 -0.626973 0.3 0.059091 -0.246497 -0.578751 0.32 0.053929 -0.258072 -0.528249 0.34 0.048556 -0.268637 -0.475666 0.36 0.042993 -0.27815 -0.421206 0.38 0.037262 -0.286574 -0.365082 0.4 0.031384 -0.293876 -0.307517 0.42 0.025384 -0.300026 -0.248735 0.44 0.019284 -0.305001 -0.18897 0.46 0.013108 -0.30878 -0.128457 0.48 0.006881 -0.31135 -0.067436 0.5 0.000627 -0.312698 -0.006147 0.52 -0.005629 -0.312821 0.055165 0.54 -0.011863 -0.311718 0.116259 0.56 -0.018051 -0.309393 0.176894 0.58 -0.024168 -0.305855 0.236828 0.6 -0.030191 -0.301118 0.295825 0.62 -0.036095 -0.295202 0.353653 0.64 -0.041857 -0.288129 0.410083 0.66 -0.047456 -0.279927 0.464894 0.68 -0.052869 -0.270629 0.51787 0.7 -0.058074 -0.260272 0.568805 0.72 -0.063052 -0.248896 0.617499 0.74 -0.067783 -0.236546 0.663763 0.76 -0.072248 -0.22327 0.707417 0.78 -0.076431 -0.209122 0.748291 0.8 -0.080314 -0.194156 0.786229 0.82 -0.083882 -0.178432 0.821084 0.84 -0.087123 -0.16201 0.852722 0.86 -0.090022 -0.144956 0.881022 0.88 -0.092568 -0.127335 0.905876 0.9 -0.094753 -0.109218 0.927188 0.92 -0.096566 -0.090674 0.944879 0.94 -0.098002 -0.071776 0.958881 0.96 -0.099054 -0.052599 0.96914
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This note was uploaded on 02/09/2012 for the course PHYSICS 152 taught by Professor Michaelfowler during the Fall '07 term at UVA.

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SimplePendulum - Simple Pendulum Spreadsheet Michael...

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